If `sqrt(5-12 i)+sqrt(-5-12 i)=z` , then principal value of `a rgz` can be `pi/4` b. `pi/4` c. `(3pi)/4` d. `-(3pi)/4`

Find the principal value of tan^(-1)tan ((3pi)/4)

If a complex number z satisfies |2z+10+10 i|lt=3sqrt(3)-5, then the least principal argument of z is a. -(5pi)/6 b. -(11pi)/(12) c. -(3pi)/4 d. -(2pi)/3

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

IF the lengths of the side of triangle are 3,5A N D7, then the largest angle of the triangle is pi/2 (b) (5pi)/6 (c) (2pi)/3 (d) (3pi)/4

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , angle, between vec aa n d vec b is (2pi)/3,| vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angel between vec aa n d vec b is a. pi/6 b. pi/4 c. pi/3 d. pi/2

If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1)a n d(dy)/(dx)=a x+b , then the value of a+b is (a) cot(pi/8) (b) cot(pi/12) (c) tan((5pi)/12) (d) tan((5pi)/8)

lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 times the eccentricity of the ellipse x^2(sec)^2alpha+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If z is a complex number lying in the fourth quadrant of Argand plane and |[(kz)/(k+1)]+2i|>sqrt(2) for all real value of k(k!=-1), then range of "a r g"(z) is a. (pi/8,0) b. (pi/6,0) c. (pi/4,0) d. none of these

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is